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Mortgage repayment lesson

Mortgage Repayment Calculator Tutorial

Learn how a repayment mortgage payment is estimated, what each calculator input means, and how to manually work through the maths before using the calculator.

Estimated time: 14 minutes

Learning objectives

  • Understand what the mortgage repayment calculator estimates and when it is useful.
  • Convert property price, deposit, rate, and term into the numbers used by the repayment formula.
  • Manually estimate a repayment mortgage payment using the standard monthly formula.
  • Interpret monthly payment, total interest, total repaid, deposit percentage, and loan-to-value as planning estimates.

Educational estimates, not advice

This tutorial explains the calculation behind a UK repayment mortgage estimate. It is designed to make calculator results easier to understand, not to recommend a mortgage product or borrowing decision.

Lesson 01

What problem the calculator solves

The repayment calculator answers a practical question: if I borrow this amount at this rate over this term, what monthly repayment might clear the mortgage?

A repayment mortgage payment is built to cover interest and gradually repay the balance by the end of the term. The calculator estimates the monthly payment, mortgage amount, LTV, total interest, and total repaid.

It is useful when you are checking a possible purchase price, comparing terms, or sanity-checking a deal before moving to a fuller mortgage comparison. It does not include lender-specific fees, insurance, taxes, or future rate changes.

Use the repayment calculatorCheck affordability first

Lesson 02

Inputs explained

The calculator starts with four core inputs: property price, deposit, annual interest rate, and mortgage term.

Property price

The home price you want to model. For a buying estimate, this is usually the agreed or expected purchase price.

Deposit

The cash going into the purchase. Property price minus deposit gives the mortgage balance.

Interest rate

The annual mortgage rate used for the estimate. The formula converts this into a monthly decimal rate.

Mortgage term

The number of years used to spread the repayments. The formula converts this into monthly payments.

Lesson 03

Formula explanation

A repayment mortgage formula sizes one regular monthly payment so the balance reaches zero at the end of the term, assuming the rate and payment stay the same.

The formula is more useful than simply dividing the loan by the number of months because interest is charged on the outstanding balance. Early in the mortgage, the balance is high, so more of the payment covers interest. Later, more of the payment reduces the debt.

The calculator uses this formula as a simplified estimate. Lenders may use daily interest, product fees, and specific payment dates, so the result should be treated as a planning figure.

Repayment mortgage formula
M = P x r / (1 - (1 + r)^-n)

M is the monthly payment, P is the mortgage balance, r is the monthly interest rate, and n is the number of monthly payments.

Worked example

Variable definitions

M
Monthly repayment
The estimated fixed monthly payment needed to clear the repayment mortgage over the chosen term if the rate stays the same.
P
Principal or mortgage balance
The amount borrowed. For a purchase estimate, this is usually property price minus deposit.
r
Monthly interest rate
The annual interest rate divided by 12 and converted from a percentage into a decimal.
n
Number of payments
The mortgage term in years multiplied by 12 monthly payments per year.

Lesson 04

Step-by-step worked example

Here is a full manual calculation for a £300,000 property, £60,000 deposit, 4.5% interest rate, and 25-year term.

Worked example

Manual repayment estimate

Repayment mortgage formula
M = P x r / (1 - (1 + r)^-n)

M is the monthly payment, P is the mortgage balance, r is the monthly interest rate, and n is the number of monthly payments.

  1. Work out the mortgage balance

    Start with the property price and subtract the deposit. This gives the amount being borrowed.

    P = £300,000 - £60,000 = £240,000

  2. Convert the annual rate into a monthly decimal

    Divide the annual rate by 12, then divide by 100 because the formula uses a decimal rate.

    r = 4.5% / 12 / 100 = 0.00375

  3. Convert the term into months

    A 25-year mortgage has 25 lots of 12 monthly payments.

    n = 25 x 12 = 300

  4. Put the numbers into the repayment formula

    Use the balance, monthly rate, and number of payments to estimate the monthly repayment.

    M = 240,000 x 0.00375 / (1 - (1 + 0.00375)^-300)

  5. Calculate the monthly payment and totals

    The monthly payment is then multiplied by the number of payments to estimate total repaid. Subtract the original balance to estimate total interest.

    Monthly payment
    About £1,334
    Total repaid
    About £400,199
    £1,333.9979 x 300, rounded.
    Total interest
    About £160,199
    Total repaid minus the £240,000 mortgage balance.

Final result

This may suggest a monthly repayment of about £1,334. Over 25 years, the simplified estimate is about £400,199 repaid in total, including about £160,199 of interest.

Lesson 05

Common Mistakes

Small input or formula mistakes can make the result look much more precise than it really is.

  • Using the annual interest rate directly in the monthly formula instead of dividing it by 12 and 100.
  • Forgetting that the mortgage balance is the property price minus the deposit, not the full property price.
  • Treating the estimate as a lender quote. Real offers may include product fees, valuation fees, insurance, rate changes, and daily interest rules.
  • Comparing monthly payments without also checking total interest, total repaid, deposit percentage, and LTV.
  • Using years for n instead of months. A 25-year term is 300 monthly payments, not 25.

Lesson 06

Calculator walkthrough

Use the calculator to test one scenario at a time, then change a single input to understand what moved the result.

  1. Enter the property price you want to test.
  2. Enter the deposit you expect to use. The calculator turns this into the mortgage amount and deposit percentage.
  3. Enter an annual interest rate. Use a realistic rate for the type of mortgage you are comparing.
  4. Enter the mortgage term in years. A longer term usually lowers the monthly payment but may increase total interest.
  5. Read the monthly repayment first, then check total interest, total repaid, and loan-to-value before comparing another scenario.
Go back to the calculator

Practice question

Exam Style Question

A buyer purchases a £275,000 home with a £55,000 deposit. The mortgage rate is 4.8% and the term is 25 years. Estimate the mortgage balance, monthly rate, number of payments, and monthly repayment using the repayment mortgage formula.

Work in stages: find P, convert the annual rate to r, convert years to n, then substitute into M = P x r / (1 - (1 + r)^-n).

Repayment mortgage formula
M = P x r / (1 - (1 + r)^-n)

M is the monthly payment, P is the mortgage balance, r is the monthly interest rate, and n is the number of monthly payments.

Full solutionShow

The mortgage balance is £220,000, the monthly rate is 0.004, the term is 300 payments, and the estimated monthly repayment is about £1,260.

  1. Find the mortgage balance

    Subtract the deposit from the purchase price.

    P = £275,000 - £55,000 = £220,000

  2. Convert the rate

    Divide the annual percentage rate by 12 and by 100.

    r = 4.8% / 12 / 100 = 0.004

  3. Convert the term

    A 25-year mortgage has 25 years of monthly payments.

    n = 25 x 12 = 300

  4. Substitute into the formula

    Use the repayment formula to estimate the fixed monthly payment before lender-specific fees or daily interest rules.

    M = 220,000 x 0.004 / (1 - (1.004)^-300)

  5. Round the result

    The formula gives a planning estimate of about £1,260 per month.

    Estimated monthly repayment
    About £1,260

Practice question

Practice questions

A buyer wants to estimate a £180,000 repayment mortgage at 6% over 20 years. What monthly payment does the formula suggest?

Try calculating the monthly rate, the number of payments, and then the monthly repayment before opening the solution.

Repayment mortgage formula
M = P x r / (1 - (1 + r)^-n)

M is the monthly payment, P is the mortgage balance, r is the monthly interest rate, and n is the number of monthly payments.

Fully worked solutionsShow

The estimated monthly payment is about £1,290. This is a simplified repayment estimate, not a lender quote.

  1. Convert the annual rate

    Divide 6% by 12 and convert it into a decimal monthly rate.

    r = 6% / 12 / 100 = 0.005

  2. Convert the term

    A 20-year term has 240 monthly payments.

    n = 20 x 12 = 240

  3. Apply the formula

    Put P = £180,000, r = 0.005, and n = 240 into the repayment formula.

    M = 180,000 x 0.005 / (1 - (1.005)^-240) = about £1,290

Practice question

Loan amount and LTV check

A home costs £250,000 and the buyer has a £25,000 deposit. What mortgage balance and loan-to-value would the repayment calculator use?

Work out the mortgage balance first, then divide it by the property price.

Second worked solutionShow

The mortgage balance is £225,000 and the loan-to-value is 90%.

  1. Subtract the deposit

    The calculator estimates the mortgage balance from the purchase price minus the deposit.

    £250,000 - £25,000 = £225,000

  2. Calculate loan-to-value

    Divide the mortgage balance by the property price, then multiply by 100.

    £225,000 / £250,000 x 100 = 90%